Remark 33 
Since the convexity of the functional \(J(\cdot )\)  is kept, the active-set Newton method summarized as Subroutine REF  is guaranteed to be convergent to a solution of (REF ). We refer to, e.g., [1]}, for rigorous analysis. Also, as analyzed in [1]}, Subroutine REF  is superlinearly convergent.

